Method for determining a queue identification number and for determining the length of the queue

ABSTRACT

A method of determining a tailback characteristic factor δ at operating stations for processing individually moving units having alternating hold-back and release phases and having a detector upstream of the respective operating station includes measuring the filling time between the hold-back start or a time instant tied to the hold-back start and continuous occupancy of the detector and subsequent comparison with a reference filling time. A first value is assigned to the tailback characteristic factor δ if the reference filling time is exceeded and a second value is assigned if the reference filling time is not exceeded.

The present invention relates to a method of determining a tailbackcharacteristic factor δ and self-calibrating methods resulting therefromfor estimating tailback lengths at operating stations for processingindividually moving units, such as, for example, traffic-lightinstallations or filters, having a detector situated upstream. Theparameters thus determined and the characteristic values derivedtherefrom may be used to control the traffic-light installation orfilters or used to display the traffic status in primary devices.

BACKGROUND OF THE INVENTION

An important matter in road-traffic technology is the determination oftailback lengths at traffic-light installations in order to obtaininformation items relating to the traffic flow. The knowledge of thetailback lengths may, in addition, serve to control the signalinstallations (Bernhard Friedrich, Methoden und Potentiale adaptiverVerfahren für die Lichtsignalsteuerung (Methods and potentials ofadaptive methods for traffic-signal control), Straβenverkehrstechnik9/1996). According to Joos Bernhard, Thomas Riedel, Erkennung von Staumit kurzen Schleifendetektoren (Detection of tailback using short loopdetectors), Straβenverkehrstechnik 7/1999, tailbacks at traffic-lightinstallations can be detected or calculated only between a stop line anddetector. The same applies also to tailbacks at any operating stationsfor processing individually moving units having alternating hold-backand release phases.

A substantial disadvantage of this known method consists in not beingable to determine tailback lengths that are greater than the distancebetween an operating station and detector.

The object of the invention is therefore to provide a method with whicha determination of the tailback length at operating stations forprocessing individually moving units is made possible not only betweenan operating station and detector in order to control a traffic-lightinstallation or filter with the aid of said tailback length orcharacteristic values derived therefrom, such as, for example, waitingtimes, or to display traffic statuses in primary devices.

BRIEF SUMMARY OF THE INVENTION

This object is achieved by a method of determining a tailbackcharacteristic factor δ, with which the tailback length can bedetermined in a simple way. In addition, other relevant parameters forthe installation control, such as, for example, the saturation timerequirement, can also be determined using said tailback characteristicfactor.

In particular, the present invention provides a method of determining atailback characteristic factor δ at operating stations for processingindividually moving units, each processing phase comprising a hold-backphase and a release phase and a detector being situated upstream of theoperating station, by measuring the time (filling time) between thehold-back start or a time instant tied to the hold-back start andcontinuous occupancy of the detector and subsequent comparison with areference filling time, wherein a first value is assigned to δ if thereference filling time is exceeded and a second value is otherwiseassigned.

A time instant coupled to a transition time before the start of thehold-back phase may also be chosen, for example, as the start of thefilling time in addition to the hold-back start. In the case of trafficlights, the amber phase would be suitable as transition time.

If the reference filling time is dropped below, that is to say if thedistance between an operating station and detector is filled morerapidly than in the reference time, a tailback may be assumed.Otherwise, the units are in free flow.

In this connection, the reference filling time is obtained, for example,from simulator tests or empirical investigations. Advantageously, thereference filling time is chosen as a function of the geometry of theinflow region, for example of the distance between a detector and afilling station, the lane width, etc., and/or of the release time of theoperating station.

Using the tailback characteristic factor δ determined in the waydescribed above, a multiplicity of relevant parameters for optimizingthroughput or a traffic status display can be determined.

A first method of estimating tailback length {circumflex over (L)}_(n)using the tailback characteristic factor determined according to theinvention in the n^(th) processing phase is based on the assumptionthat, as a linear function of a smoothed tailback characteristic factor{circumflex over (δ)}_(n) that is determined from the tailbackcharacteristic factor δ_(n) taking into account the (n−1)^(th) smoothedtailback characteristic factor {circumflex over (δ)}_(n−1), {circumflexover (L)}_(n) is given by:{circumflex over (L)} _(n)({circumflex over (δ)}_(n))=m{circumflex over(δ)} _(n,)  (1)where {circumflex over (δ)}_(n) may no longer assume only two values,but a plurality of values. With a Specified m, the tailback length for agiven {circumflex over (δ)}_(n) is given by equation (1). The tailbackcharacteristic factor is smoothed in order to avoid excessively largechanges in the tailback characteristic factor from one processing phaseto the next.

This method is distinguished by the fact that speed measurements are notnecessary to determine the tailback length.

Advantageously, the slope is readjusted in each n^(th) processing phase.For this purpose, the traffic level q_(n) is determined. This is given,for example, by an estimate or by the measured number of units that passthe detector during the n^(th) processing phase. It can be calculatedfrom the traffic level how many units were present during the n^(th)hold-back phase at least upstream of the operating station; a lowerlimit L_(n) ⁰ is consequently obtained for the tailback length. On theother hand, the tailback-length function of the previous processing step{circumflex over (L)}_(n−1)({circumflex over(δ)}_(n))=m_(n−1){circumflex over (δ)}_(n) with {circumflex over(δ)}_(n) and a suitably chosen m_(n−1) yields an estimate of the actualtailback length in the current processing phase. By comparing L_(n) ⁰and {circumflex over (L)}_(n−1)({circumflex over (δ)}_(n)), m_(n) and,consequently, {circumflex over (L)}_(n) can be calibrated.

The slope of the (n−1)^(th) processing phase is advantageously obtainedby recursive application of the method just described with suitablestarting values for {circumflex over (δ)}₀ and m₀. This method isconsequently self-calibrating.

Preferably, the tailback characteristic factor is smoothed by forming aconvex combination of the current tailback characteristic factor and thesmoothed tailback characteristic factor of the previous processing:{circumflex over (δ)}_(n)=αδ_(n)+(1−α) {circumflex over (δ)}_(n−1),α∈[0,1]  (2)

The traffic level q_(n) is preferably measured using the detectorlocated upstream of the operating station.

In an advantageous version, the lower limit of the tailback length L_(n)⁰ is given as a linear function of q_(n) since even this simple form isa good approximation. Preferably, the slope of this straight linedepends on the time in which the detector is continuously occupiedduring a portion of the processing phase. If this dependence is takeninto account, the agreement with real data is improved.

It is advantageous to alter the slope m_(n) only if either δ_(n) hasassumed the second value and L_(n) ⁰>{circumflex over(L)}_(n−1)({circumflex over (δ)}_(n))=m_(n−1){circumflex over (δ)}_(n)or if δ_(n) has assumed the first value and L_(n) ⁰<{circumflex over(L)}_(n−1)({circumflex over (δ)}_(n))=m_(n−1){circumflex over (δ)}_(n).In the first case, δ_(n) shows, on the one hand, a tailback at adistance of at least L_(n) ⁰ from the operating station and, on theother hand, the estimate of the tailback length {circumflex over(L)}_(n−1)({circumflex over (δ)}_(n)) is below L_(n) ⁰. In the secondcase, although δ_(n) does not indicate a tailback of length L_(n) ⁰, thetailback is, on the other hand, still longer than L_(n) ⁰ according tothe estimate {circumflex over (L)}_(n−1)({circumflex over (δ)}_(n)). Inboth cases, therefore, it is appropriate to calibrate the slope m_(n).If, on the other hand, the value of the tailback characteristic factorand the estimated tailback length are not inconsistent, the slope isretained: m_(n)=m_(n−1).

To adapt the slope m_(n), a smoothed tailback length L′_(n) may be usedthat results as a combination of L_(n) ⁰ and {circumflex over(L)}_(n−1)({circumflex over (δ)}_(n)):L _(n) ′−βL _(n) ⁰ (q _(n))+(1−β){circumflex over (L)}_(n−1)({circumflex over (δ)}_(n)), β>0  (3)

The tailback characteristic factor δ determined by the method accordingto the invention described above may also be used to determine thesaturation time requirement; this is the average time requirement valueof a unit in saturated (no longer free) flow during the release phase.The saturation time requirement is, on the one hand, a measure of theperformance of the operating station. On the other hand, it may alsoserve to estimate tailback length by means of a queuing model.

To determine the saturation time requirement t_(n) ^(B) in the n^(th)processing step, the tailback characteristic feature δ is firstdetermined using the method according to the invention and the trafficlevel q_(n) is measured or estimated. The saturation time requirementcan then be calculated, using a suitable starting condition for t₀ ^(B),by means of

$\begin{matrix}{t_{n}^{B} = \{ \begin{matrix}{\frac{t_{n}^{q}}{q_{n}},} & {{{{if}\mspace{20mu}\delta_{n}} = {\delta_{n - 1}\mspace{14mu}{is}\mspace{14mu}{equal}\mspace{14mu}{to}\mspace{14mu}{the}\mspace{14mu}{second}\mspace{14mu}{value}}},} \\{t_{n - 1}^{B},} & {{otherwise}.}\end{matrix} } & (4)\end{matrix}$where t^(g) _(n) is the release time in the n^(th) processing step.

In order to avoid excessively large changes in the saturation timerequirement from one processing step to the next, only a specifiedmaximum change Δt^(B) _(max)>0 of the saturation time requirement ispreferably permitted in each step. If, therefore, the t_(n) ^(B)obtained from equation (4) fulfils one of the inequalities:Δt ^(B) −t ^(B) _(n) −t ^(B) _(n−1) >Δt ^(B) _(max) or Δt ^(B) <−Δt ^(B)_(max)  (5)a modified saturation time requirement {circumflex over (t)}^(B) _(n) isadvantageously calculated, where{circumflex over (t)} ^(B) _(n) =t ^(B) _(n−1) +Δt ^(B) _(max) or{circumflex over (t)} ^(B) _(n) =t ^(B) _(n−1) −Δt ^(B) _(max)  (6)

It is advantageous to measure the traffic level q_(n) using the detectorsituated upstream of the operating station.

As an alternative to the method according to the invention describedabove, the tailback length can be determined with the aid of a queuingmodel that comprises an inherent model saturation time requirement τ^(B)_(n) having a suitably chosen start value as parameter to be calibrated.Such a method may comprise in any nth processing operation:

Next, the actual saturation time requirement t^(B) _(n) is determined inaccordance with the method according to the invention described above.If the saturation requirement value of the last processing phase changesby Δt^(B), the inherent model saturation requirement valuo τ^(B) _(n) isadapted usingτ^(B) _(n)=τ^(B) _(n−1) +c _(d) Δt ^(B)  (7)where C_(d) denotes a suitably chosen damping constant. In particular,the inherent model saturation requirement value is adapted usingτ^(B) _(n)=τ^(B) _(n−1) +c _(d)sgn(Δt ^(B))min{|Δt ^(B) |, Δt ^(B)_(max)}  (8)if only a maximum change of Δt^(B) _(max) is permitted for the actualsaturation requirement value, where sgn(Δt^(B)) denotes the sign ofΔt^(B). A lower limit for the tailback length L⁰ _(n) is calculated fromthe traffic level. Using these quantities, a first estimate of thetailback length L″_(n) is calculated with the aid of a queuing model.Then L″_(n) and L⁰ _(n) are compared in a way analogous to the abovemethod of tailback length estimation. If L″_(n)>L⁰ _(n) and δ_(n) hasassumed the first value or if L″_(n)<L⁰ _(n) and δ_(n) has assumed thesecond value, the inherent model saturation time requirement has to bemodified. Using the calibrated model saturation time requirement, acalibrated estimate of the tailback length is then calculated using thetailback model.

This method is distinguished in that no speed measurements are necessaryfor determining the tailback length.

Furthermore, faults in the outflow can advantageously be taken intoaccount and a suitably modified traffic level used in the queuing model.

In a beneficial version of the fault compensation, q_(n) is modifiedonly if it is less than the second-largest value max_(10.2) (q) of thelast ten q values. In this case, a time interval during the processingphase is chosen to calculate the fault compensation and predetermined,shorter time intervals, for example the full seconds in which thedetector is continuously occupied in the total interval, are counted.The entire interval preferably begins a few seconds after the start ofthe release phase and finishes a few seconds after the end of therelease phase. If the number thus obtained is divided by the length ofthe entire interval, the degree of occupancy b ∈ [0,1] of the detectoris obtained. If b drops below a lower limit u, the value 0 is assignedto a fault characteristic factor s. If b exceeds an upper limit o, thevalue 1 is assigned to s. If u≦b≦o, s is given by

$\begin{matrix}{s = \frac{b - u}{o - u}} & (9)\end{matrix}$

As a modified traffic level q′nq′ _(n) =q+s(1+P _(comp))(max_(10.2)(q)−q)  (10)is then taken, where P_(comp) is a constant with which the level of thefault compensation can be adjusted.

The inherent model saturation time requirement is advantageouslycalibrated using a feedback method based on a conventional PID regulator(proportional-integral-differential regulator). For this purpose, −1should be assigned to δ_(n) as the first value (if there is no tailback)and 1 should be assigned as the second value (if there is a tailback).The calibration uses two variables: {tilde over (s)}_(n) (corresponds toa sawtooth integrating term) and {tilde over (d)}_(n) (corresponds to adifferentiating member). If δ_(n)L″_(n)≧δ_(n)L⁰ _(n), {tilde over(s)}_(n)={tilde over (d)}_(n)=0 and the saturation time requirement isunaltered. Otherwise, the auxiliary variable

$\begin{matrix}{A = {\frac{t_{n}^{B}}{t_{n}^{g}}( {L_{n}^{''} - L_{n}^{0}} )}} & (11)\end{matrix}$is defined.

In order to avoid overcorrecting the saturation time requirement,A′=sgn(A)min{|A|, 1}  (12)can be defined, where sgn(A) denotes the sign of A. There are now chosen

$\begin{matrix}{{\overset{\sim}{s}}_{n} = \{ {\begin{matrix}{{{\overset{\sim}{s}}_{n - 1} - \delta_{n}},} & {{{if}\mspace{20mu}{\overset{\sim}{s}}_{n - 1}\delta_{n}} < 0} \\{{- \delta_{n}},} & {{otherwise}\mspace{40mu}}\end{matrix}{and}} } & (13) \\{{\overset{\sim}{d}}_{n} = \{ \begin{matrix}{\frac{{\overset{\sim}{d}}_{n - 1}}{t_{d}},} & {{{if}\mspace{20mu}{\overset{\sim}{d}}_{n - 1}\delta_{n}} < 0} \\{{- \delta_{n}},} & {{otherwise}\mspace{40mu}}\end{matrix} } & (14)\end{matrix}$where t_(d) is a constant to be suitably chosen. This then yields thecalibrated saturation time requirement for the queuing model{tilde over (τ)}^(B) _(n)=τ^(B) _(n)−(p _(p) A′+|A′|(p _(i) {tilde over(s)} _(n) +p _(d) {tilde over (d)} _(n)))  (15)where p_(p), p_(i) and p_(d) denote the parameters of the regulator.

It is advantageous to smooth the calculated tailback length by forming aconvex combination of L⁰ _(n) and L″_(n):L _(n) =γL ⁰ _(n)+(1−γ)L″ _(n), γ∈[0,1].  (16)

This avoids an overcorrection of the tailback length.

Two methods according to the invention of determining the tailbacklength estimation with the aid of the method according to the inventionof determining the tailback characteristic factor are described belowwith reference to the drawing. In the drawing:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the calculated slope m_(n) of the tailback-length functionas a function of time from method 1,

FIG. 2 shows the estimated tailback (in vehicles) as a function of theexplicitly measured, smoothed tailback from method 1,

FIG. 3 shows the estimate of the tailback time requirement t^(B) _(n) asa function of time from method 2.

DETAILED DESCRIPTION OF THE INVENTION

Method 1

The application of the method of tailback length estimation and itsverification is shown at an approach to a heavily loaded traffic-lightinstallation (in the town direction of theLandsberger/Trappentreustrasse, Munich) with strongly varying greentimes (release times).

The detector is located 30 m or approximately 5 vehicles away from thestop line. As a reference filling time for this distance, 22 seconds isassumed.

If the reference filling time is exceeded, the value 0 is assigned to δand otherwise, the value 1 is assigned. The tailback characteristicfactor is smoothed in that {circumflex over(δ)}_(n)=αδ_(n)+(1−α){circumflex over (δ)}_(n−1), where α is typicallybetween 0.05 and 0.2 and δ₀={circumflex over (δ)}₀=0.

The lower limit is calculated by means ofL ⁰ _(n) =q _(n)√{square root over (1−min(γ₁ , bγ ₂))}+α₁γ_(i)≧0,  (17)where α₁ takes account of the vehicles between the detector and stopline and therefore assumes the value α₁=5. In this exemplary embodiment,γ₁ is chosen as =0.9 and γ₂ is chosen as =1.2. The degree of occupancy bof the detector is obtained by counting the full seconds between 5 safter the start of release and 15 s after the end of release in whichthe detector is continuously occupied, and then dividing by the totallength of this time interval; consequently, b is always ∈[0,1].

The slope m_(n) is written as m_(n)=m′_(n)/m″_(n) in this example, wherem′₀=10 and m″₀=0.5 form suitable start values. The slope is modified bymeans of a smoothed value

L′_(n)=βL⁰ _(n)(q_(n))+(1β){circumflex over (L)}_(n−1)({circumflex over(δ)}_(n)), where β=0.7. It is the case that

$\begin{matrix}{m_{n}^{\prime} = \{ {\begin{matrix}{\frac{{( {k_{n - 1} - 1} )m_{n - 1}^{\prime}} + {{\hat{\delta}}_{n}L_{n}^{\prime}}}{k_{n - 1}},} & {{if}\mspace{14mu}{the}\mspace{14mu}{values}\mspace{14mu}{of}\mspace{14mu}\delta\mspace{14mu}{and}\mspace{14mu} L_{n}^{0}\mspace{14mu}{are}\mspace{14mu}{inconsistent}} \\{m_{n - 1}^{\prime},} & {{otherwise},}\end{matrix}{and}} } & (18) \\{m_{n}^{''} = \{ {\begin{matrix}{\frac{{( {k_{n - 1} - 1} )m_{n - 1}^{''}} + {\hat{\delta}}_{n}^{2}}{k_{n - 1}},} & {{if}\mspace{14mu}{the}\mspace{14mu}{values}\mspace{14mu}{of}\mspace{14mu}\delta\mspace{14mu}{and}\mspace{14mu} L_{n}^{0}\mspace{14mu}{are}\mspace{14mu}{inconsistent}} \\{m_{n - 1}^{''},} & {{otherwise},}\end{matrix}{where}} } & (19) \\{k_{n} = \{ \begin{matrix}{{\min\{ {{k_{n - 1} + 1},K} \}},} & {{if}\mspace{14mu}{the}\mspace{14mu}{values}\mspace{14mu}{of}\mspace{14mu}\delta\mspace{14mu}{and}\mspace{14mu} L_{n}^{0}\mspace{14mu}{are}\mspace{14mu}{inconsistent}} \\{k_{n - 1},} & {{otherwise},}\end{matrix} } & (20)\end{matrix}$

Suitable values for a fast, but stable estimate are k₀=10 and K=1000.

FIG. 1 shows the calibration of the slope m_(n). The arbitrarilyspecified value of approximately 20 increases on the first day to thovalue that corresponds to the traffic characteristic of the lane. Onlyslight adaptation processes then occur. The control behaviour is stableand robust.

FIG. 2 shows the comparison of the estimated, smoothed tailback lengthwith manually increased, slightly smoothed tailback length values. Themeasured tailback L^(real) _(n) was smoothed using{circumflex over (L)} ^(real) _(n)=0.3L ^(real) _(n)+0.7{circumflex over(L)} ^(real) _(n−1)  (21)

A squared correlation coefficient of R²=0.7748 indicates a goodrelationship between estimated and real tailback length.

Method 2

As an application of the method, the determination of the tailbacklength at the approach mentioned in the above example to a traffic-lightinstallation is described with the aid of a queuing model.

To calculate the saturation time requirement, a maximum change of Δt^(B)_(max)=0.02 is permitted. The change is additionally damped in thequeuing model by the factor c_(d)=0.9.

FIG. 3 shows the determination of the time requirement value t^(B) _(n)as a function of time for a start value of t^(B) ₀=2s. It can be seenthat, in addition to the transient oscillation process, fluctuationsoccur in t^(B) _(n) several times within the two working days. Thesefluctuations are explained, inter alia, by variable traffic patterns anddriving behaviour of road users that is dependent on the time of day.

Faults in the outflow are compensated by means of the degree ofoccupancy known from the above example. The fault characteristic factors is given by equation (9), where u=0.2 and o =1.1 are used for thelimits. This choice guarantees that s is always less than 1.

In this example, the macroscopic queuing model is taken from R. M.Kimber and E. M. Hollis, Traffic queues and delays at road junctions,TRRL Laboratory Report 909, Berkshire, 1979. The model equation for thetailback length L is

$\begin{matrix}{{L = {\frac{1}{2}( {\sqrt{A^{2} + B} - A} )}}{where}} & (22) \\{{A = \frac{\begin{matrix}{{( {1 + {q\frac{\tau^{B}}{t_{n}^{g}}}} )( \frac{t_{n}^{g}}{\tau^{B}} )^{2}} +} \\{{( {1 - L_{n - 1}} )\frac{t_{n}^{g}}{\tau^{B}}} - {2( {1 - C} )( {L_{n - 1} + q} )}}\end{matrix}}{\frac{t_{n}^{g}}{\tau^{B}} + ( {1 - C} )}}{and}} & (23) \\{B = \frac{4( {L_{n - 1} + q} )( {\frac{t_{n}^{g}}{t^{B}} - {( {1 - C} )( {L_{n - 1} + q} )}} )}{\frac{t_{n}^{g}}{\tau^{B}} + ( {1 - C} )}} & (24)\end{matrix}$where C=0.6 characterizes the statistical fluctuations in the outflow.

Suitable parameters for calibrating the saturation time requirementanalogously to a PID controller are p_(d)=0.003, p_(i)=0.01, p_(d)=0.01and t_(d)=1.2.

The tailback-length estimate is smoothed using γ=0.6.

1. Method of determining a tailback characteristic factor δ at operatingstations for processing individually moving units having alternatinghold-back and release phases and having a detector upstream of therespective operating station by measuring the filling time between thehold-back start or a time instant tied to the hold-back start andcontinuous occupancy of the detector and subsequent comparison with areference filling time, in which method a first value is assigned to thetailback characteristic factor δ if the reference filling time isexceeded and a second value is assigned if the reference filling time isnot exceeded.
 2. Method according to claim 1, in which the referencefilling time is chosen as a function of the geometry of the inflowregion of the operating station.
 3. Method according to claim 1, inwhich the reference filling time is chosen as a function of the releasetime.
 4. Method of determining the saturation time requirement t_(n)^(B), which corresponds to the average time requirement of a unit withsaturated flow during the release phase, by (a) determining the tailbackcharacteristic factor according to claim 1, (b) determining the trafficlevel q_(n), (c) determining the saturation time requirement t_(n) ^(B)using the release time t_(n) ^(q) and a suitable starting condition fort₀ ^(B) in accordance with $t_{n}^{B} = \{ \begin{matrix}{\frac{t_{n}^{g}}{q_{n}},} & {{{{if}\mspace{14mu}\delta_{n}} = {\delta_{n - 1}\mspace{14mu}{is}\mspace{14mu}{equal}\mspace{14mu}{to}\mspace{14mu}{the}\mspace{14mu}{second}\mspace{14mu}{value}}},} \\{{t_{n - 1}^{B},}\;} & {{otherwise}.}\end{matrix} $
 5. Method according to claim 4, in which thesaturation time requirement t^(B) _(n) is altered in each nth processingphase by not more than a predetermined maximum value compared with thesaturation time requirement of the (n−1)^(th) processing phase. 6.Method according to claim 4, in which the traffic level q_(n) ismeasured with the detector upstream of the operating station.
 7. Methodof determining the tailback length L″_(n) by (a) determining thesaturation time requirement t^(B) _(n) according to claim 4, (b)determining an inherent model saturation time requirement τ^(B) _(n) inaccordance with τ_(n) ^(B)=τ^(B) _(n−1)+c_(d)(t^(B) _(n)−t^(B) _(n−1))using an (n−1)^(th) model saturation time requirement τ^(B) _(n−1) andwith a suitably chosen C_(d), (c) calculating a lower limit of thetailback length L_(n) ⁰ as a function of q_(n), (d) calculating atailback length estimation with a queue model using the inherent modelsaturation time requirement, (e) calibrating the inherent modelsaturation requirement by comparing the tailback length estimation withthe lower limit L_(n) ⁰, (f) calculating the tailback length L_(n)″ witha queuing model using the calibrated inherent model saturation timerequirement.
 8. Method according to claim 7, in which the tailbacklength calculation is made with a modified traffic level that takesaccount of faults in the outflow.
 9. Method according to claim 8, inwhich the flow compensation is calculated by counting in a time intervalduring the processing phase predetermined time intervals, in particularcomplete seconds, in which the detector is continuously occupied. 10.Method according to claim 7, in which the inherent model saturation timerequirement is calibrated using a classic PID controller method. 11.Method according to claim 7, in which the tailback length estimation issmoothed by forming a convex combination of L_(n) ⁰ and L_(n)″ inaccordance with L_(n)=γL_(n) ⁰+(1−γ) L_(n)″, γ∈[0,1].
 12. Method ofdetermining the tailback length {circumflex over (L)}_(n) in the nthprocessing phase by (a) determining the nth tailback characteristicfactor δ_(n) according to claim 1, (b) calculating a smoothed tailbackcharacteristic factor {circumflex over (δ)}_(n) using the (n−1)^(th)smoothed tailback characteristic factor {circumflex over (δ)}_(n−1), (c)determining the tailback length {circumflex over (L)}_(n) ({circumflexover (δ)}_(n))=m{circumflex over (δ)}_(n) with suitably predeterminedslope m.
 13. Method according to claim 12, wherein the slope m_(n) isdetermined in the nth processing phase by (a) determining the trafficlevel q_(n), (b) calculating a lower limit L_(n) ⁰ for the tailbacklength as a function of q_(n), (c) determining the slope m_(n) bycomparison of L_(n) ⁰ with {circumflex over (L)}_(n−1) ({circumflex over(δ)}_(n)) with a suitably predetermined slope m_(n−1).
 14. Method inwhich the slope m_(n−1) is determined by recursive application of themethod according to claim 13 with suitable starting conditions for m₀and {circumflex over (δ)}₀.
 15. Method according to claim 13, in whichthe traffic level q_(n) is measured with a detector situated upstream ofthe operating station.
 16. Method according to claim 13, in which thelower limit L_(n) ⁰ of the tailback length is predetermined as a linearfunction of q_(n).
 17. Method according to claim 16, in which the slopeL_(n) ⁰(q_(n)) is predetermined as a function of the time, in which thedetector is continuously occupied during a portion of the processingphase.
 18. Method according to claim 13, in which the slope m_(n), isaltered with respect to m_(n−1) if the second value is assigned to δ_(n)and L_(n) ⁰>{circumflex over (L)}_(n−1) ({circumflex over(δ)}_(n))=m_(n−1){circumflex over (δ)}_(n) or if the first value isassigned to δ_(n) and L_(n) ⁰<{circumflex over (L)}_(n−1)({circumflexover (δ)}_(n))=m_(n−1){circumflex over (δ)}_(n) and otherwisem_(n)=m_(n−1) is set.
 19. Method according to claim 13, in which theslope m_(n) is adapted by means of a smoothed valueL _(n) ′=βL _(n) ⁰(q _(n))+(1−β){circumflex over (L)} _(n−1)({circumflex over (δ)}_(n)) where β>0.
 20. Method according to claim 12,in which the smoothed tailback characteristic factor {circumflex over(δ)}_(n) is calculated as a convex combination of δ_(n) and {circumflexover (δ)}_(n−1) in accordance with {circumflex over(δ)}_(n)=αδ_(n)+(1−α){circumflex over (δ)}_(n−1), α∈[0,1].